Question: Solve for $x$ and $y$ using elimination. ${5x+3y = 49}$ ${-4x+3y = 4}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${5x+3y = 49}$ $4x-3y = -4$ Add the top and bottom equations together. $9x = 45$ $\dfrac{9x}{{9}} = \dfrac{45}{{9}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {5x+3y = 49}\thinspace$ to find $y$ ${5}{(5)}{ + 3y = 49}$ $25+3y = 49$ $25{-25} + 3y = 49{-25}$ $3y = 24$ $\dfrac{3y}{{3}} = \dfrac{24}{{3}}$ ${y = 8}$ You can also plug ${x = 5}$ into $\thinspace {-4x+3y = 4}\thinspace$ and get the same answer for $y$ : ${-4}{(5)}{ + 3y = 4}$ ${y = 8}$